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Illegal prime (wikipedia.org)
267 points by deadghost 9 months ago | hide | past | web | favorite | 192 comments



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Call the cops.


Plain text is already a numeric encoding of information. Any file is just a big number in binary. If it is illegal for me to sell your credit card number in plaintext then surely the same should apply to encoding the same information in some other trivial way. Talking about "illegal primes" is supposed to make it sound ridiculous, but you could just call it illegal information exchange. Most people would agree at least some forms of information exchange should be illegal - threats, stolen passwords or stolen private pictures for example.

Context and intention matters for the law - if your message is a numerically encoded death threat and the intended recipient already knows how to decode it (e.g because you sent the key in a previous message) then it would be reasonable to call the cops.

Whether the CSS key should be illegal to share is a different discussion.


Thank you. I've struggled to explain this concept to my friends and acquaintances -- your wording makes the point very clear.


This line of argument is rather asinine - any information can obviously be encoded into a number, prime or otherwise. Given that there are infinite primes and any amount of proscribed information (national security information, child pornography, trade secrets etc) that can be encoded into them, essentially all prime numbers would be deemed "illegal" under that line of argument.

The authors are clearly targeting unsophisticated audience with that article; feels like the "sovereign citizen" grade of legal analysis.


> This line of argument is rather asinine - any information can obviously be encoded into a number, prime or otherwise. Given that there are infinite primes and any amount of proscribed information (national security information, child pornography, trade secrets etc) that can be encoded into them, essentially all prime numbers would be deemed "illegal" under that line of argument.

I think its asininity (or whatever) is the point. The idea that information can be illegal leads, I think ineluctably, to the 'illegal primes'; so I think that this is meant as a slightly snarky argument against the idea that information can be illegal.


Is the article making much of an argument? It's a wikipedia article and is therefore written in an encyclopedic tone. Do you disagree that illegal numbers exist?


It has an "encyclopedic tone" but that does not mean it is objectively correct or makes a sensible argument. It is not the number itself that is illegal. What would that even mean? Humans doing certain things with certain intentions can be illegal.

The article links to "illegal numbers", which weasely states "if communicating a specific set of information is illegal in some way, then the number may be illegal as well". Note the "may", and the only references seem to be pure speculation.

Some people argue any kind of copyright and IP rights should be abolished, but who would argue it should be completely legal to phone in a bomb threat because "it is really just a number represented as sound"?


> Do you disagree that illegal numbers exist?

Well yes, the notion of illegal numbers is a construct of the silly argument presented. You can decompose anything proscribed into the elements that make it up and then try to claim the elements are ipso facto proscribed.

Mens rea, for example, is really referring to sequences of electrical impulses in your brain, so again by the line of argument there is a physical phenomenon that is criminial.


Excellent point. To put it another way, all Facebook did was to share some numbers with Cambridge Analytical who did some math with those numbers and shared those further with the Trump campaign. Why is everybody upset over math?


Context is everything. The number 123456789 is not illegal.

But if associated with other information such that this value is understood to be a social security number (if it were a valid SSN), it becomes illegal to share it, or even have it, in some circumstances.


SSNs are sequential; the numbers adjacent to your own are valid. Surely you cannot bypass data privacy requirements by applying a trivial and reversible transportation like +/- 1, so knowledge of your own social security number would be illegal under your logic.

It doesn’t make sense to think of SSNs as stolen identities unless the thief knows the names associated with them.


I thought my second sentence addressed this.


seems, from the comments, like it’s time for another generation of developers to read What Colour Are Your Bits: http://ansuz.sooke.bc.ca/entry/23


The article is based on a false premise. The government does not make any bits legal or illegal. It prohibits specific human actions: copying, selling, using, etc.

Bits have no color. But human beings do different things in order to develop different bit sequences. Take the bit sequence corresponding to a movie. The bits have no color. But that’s irrelevant. What matters is what you did to get that information. If you can prove that the bits came from an RNG that’s not copyright infringement. Likewise, if you recompress a file you copied and totally change the bit sequence, it’s still infringement. The law doesn’t care about the bits; they are tangential to human actions.

Saying that “certain bit sequences are illegal” is reductio ad absurdum like saying that laws against battery amount to making certain sequences of muscle fiber contractions illegal. The law doesn’t care about the muscle fibers that contracted; that is entirely incidential to the fact that you punched someone.


What is the false premise? The linked article http://ansuz.sooke.bc.ca/entry/23 is saying the same thing you are, with an in-depth explanation.

The article isn't great in how it explains, and it's unfriendly toward the legal profession, but it makes the same claims you do.

rayiner: > If you can prove that the bits came from an RNG that’s not copyright infringement.

article: > It doesn't matter that it looks like, or maybe even is bit-for-bit identical with, some other file that you could get from a random number generator. It happens that you didn't get it from a random number generator.


The false premise is that the law cares about any combination of bits and/or metadata. Even talking about "provenance" is misleading, because that puts the focus on the data.

The law regulates human conduct; crimes require a human action combined with a human state of mind. Things (bits, guns, etc.) are relevant to the extent that people take actions with them. To address the RNG example: the law doesn't care about whether the bits came from an RNG or an original copy per se. The law cares about those things only to the extent that they imply that someone generated the bits randomly versus copying them from the original. (Note the focus on verbs.)

In the RNG example the distinction does not matter, but consider something like insider information about an upcoming merger. The provenance is a leak from someone inside the company. Whether it is legal or illegal depends on what you do with it (trade on it versus publish it), and what you were thinking when you did it (even if you trade on it, if you didn't know it was insider information then there is no crime).


And yet quantitatively, these "Illegal primes" aren't anywhere near the information content of a movie.

We can try applying your narrative to the number 3.14, supposing laws had made finding the circumference of a circle illegal. Sure, "3.14" isn't illegal on its own (and sometimes it even shows up in the amount of change you're owed). But referencing the number is basically referencing a specific use. And so we can infer that the people broadcasting the number are doing so to highlight how easy finding the circumference of a circle is, and thus induce people to do so.

The informational content of 3.14 is say 12 bits and the original AACS key is 128 bits. Whereas a movie is roughly 10,000,000,000 bits, and even a song is around 32,000,000 bits. These "illegal primes" are very close, if not in, the domain of bona fide facts. And the law generally doesn't criminalize facts (like 3.14), although not for lack of trying!


> We can try applying your narrative to the number 3.14, supposing laws had made finding the circumference of a circle illegal.

> The informational content of 3.14 is say 12 bits and the original AACS key is 128 bits.

3.14 is irrelevant for finding the circumference of a circle (from its radius, I guess you meant); it is π that is relevant for finding the circumference, and (conjecturally) the informational content of π is infinite.


I knew I was bound to get this type of comment. The error resulting from representing pi as 3.14 is much less than the PSNR resulting from representing a feature movie using 10Gb. Be thankful I didn't use "3".


> I knew I was going to get this type of comment. The error resulting from representing pi as 3.14 is much less than the PSNR resulting from representing a common movie using 10Gb. Be thankful I didn't use "3".

The comment may have been predictable, but it doesn't seem to me to be invalid. The error resulting from representing π as 3.14 is relatively small numerically, but, in terms of information loss, it is (conjecturally) infinite. (The information encoded in the 1000th decimal place is, information-theoretically though not numerically, just as significant as that encoded in the 1st decimal place.) It therefore seems to me to be false that it is much less than the (finite) error resulting from representing a common movie using 10 Gb.


Uncompressability doesn't imply information content, for example the output of a stream cipher. I believe the digits of pi can be calculated algorithmically, no? That program is a bound on the information content of pi.

You can make a similar argument about digitizing film via sampling, rather than digitally recording the state of every atom - you're throwing away a huge amount of information. Not infinite of course, but dwarfing what it takes to accurately represent the movie. That's a philosophical curiosity, but not really relevant to the qualitative situation.

My point with 3.14 was that everybody recognizes it as a reference to pi, and it works well enough to calculate the circumference of a circle in an engineering context.

(FWIW I personally hate "Pi Day" as March 14th, as it reeks of numerology. It should probably be the day/time when the Earth has traveled around the sun its distance from the sun)


> I believe the digits of pi can be calculated algorithmically, no? That program is a bound on the information content of pi.

Yes, good point. I was using the term informally, and probably incorrectly, to mean that π (conjecturally) contains any finite string of digits (in any base)—what is formally called 'normality' (https://en.wikipedia.org/wiki/Normal_number). Apropos of your correct belief, there's a lovely so called 'spigot algorithm' due to Bailey–Borwein–Plouffe that can generate any hexadecimal digit of π that you please without having to generate intermediate digits: https://en.wikipedia.org/wiki/Bailey–Borwein–Plouffe_formula .


> FWIW I personally hate "Pi Day" as March 14th, as it reeks of numerology. It should probably be the day/time when the Earth has traveled around the sun its distance from the sun

Incidentally, wouldn't that be the less compelling "1 radian day"? Also, to celebrate such a day, we'd have to decide: travelled since when?, and then we're right back to arbitrariness (why choose January 1, or whatever other date/time is chosen)?

For me, while it's hardly an accurate picture of what math is or why it matters, I'm happy enough to have anything that gives people a positive impression of mathematics.


You are talking about the "content" bits. These illegal primes do not represent copyrighted/authored works, they are the secret decoding keys (remember DeCSS?) that are crucial to securing certain forms of DRM. As such, they are more like trade secrets. But trade secrets don't have much legal protection, so the industry got wise and helped write some new laws (to call them copyright, among other things) and can now further protect/entrench themselves.


This is gzipped C code, which is "content bits."


OK, I may have missed that, but not all illegal primes are content, so not all of them are subject to the copyright legal regime. Hence, the DMCA exists to close those gaps by declaring new kinds/classes of numbers to be illegal.


Came here to repost exactly that, thanks! I second the recommendation - this piece contains insights crucial to understand the perspective of the law wrt. all things digital.

If I were to shorten it to one sentence, it would be this: the law doesn't deal with static, mathematical reality. It considers provenance.


Ooh, got to love any article about intellectual property that starts with a analogy to the game Paranoia.


Well thank you, that was a really good read. And so seems to be the rest of the author’s work!


As computer scientists and hackers at heart, we all know that text, numbers, pictures, music, movies can be represented in each other (most likely, everything ist represented as a list of numbers, i.e. a bytestring, i.e. a file, nowadays).

The interesting part here is the obvious contradiction that prime numbers seem innocent but in the end, they are numbers, and numbers can represent anything.

Again, the obvious question to rise here is: How is it possible that a government can forbid information?


The subtle thing that I think the notion of 'illegal prime' misses is that it's not actually the prime number that is illegal.

To complete the 'illegality' you need three pieces of information used in tandem:

1) the prime number (which is innocent in its own right)

2) the decompression algorithm (also innocent in its own right)

3) the knowledge that some specific prime number, when viewed through the lens of the decompression algorithm, yields an 'illegal' interpretation. (not illegal in its own right?)

The issue only comes from all three being present. If you have #2 and #3, #1 can be the last puzzle piece needed to create the required set, but no one piece is in-and-of-itself the source of the issue.


I think you need a fourth element: intent to produce the illegal representation.

Of course, if the compression algorithm is one that's very commonly used like gzip or jpeg, a jury will infer intent from the totality of the circumstances and your lawyer will have a really hard time talking them out of it.


Most techies seem to take away the lesson you’re positing here. But it seems to me that the real lesson is that “is prime” and “is innocent” are orthogonal concepts. Why is it so strange that some prime numbers represent data you’re not allowed to distribute or even possess? Primes aren’t that rare. “Illegal prime” isn’t much different from “illegal odd number” or “illegal number where exactly half the bits are set to 1.”


Yeah, totally. It's entirely reasonable that governments can restrict SOME kind of information exchange, and since all information is just numbers, of course you could find "illegal primes"

For instance, if you encoded the entire design of a nuclear weapon (or some other highly classified military secret) inside a prime, saying "but it's just a prime!" is a very silly excuse for exchanging that information. The question is: "what kind of information should be illegal to exchange", not "which format of information should be protected".


In my opinion, I don't think it's the number itself that's illegal, but the metadata that you attach to it.

"11234349387298245791029384857" may or may not be an illegal number. Nobody cares and mathematicians can use it to their heart's content. That is, until I attach the metadata to it: "This number is the AES key embedded in every YthnVideo Disc Player". Now it's illegal. Number = legal. Number + metadata = illegal.

At least, that's how it should be.


The tricky bit there is in how metadata may come to be attached. If there exists a list of web pages, each of which contains a single prime number, then that list is legal, yes?

If from a completely different domain, someone who has no relationship whatsoever to the maintainer of that first site creates a page explaining how DVD players contain AES keys and then links to one of the pages on the first page, from the perspective of a web user, that's number + metadata = illegal, right? And yet the number itself is legal. And the text by itself is legal. The combination is illegal, but the combination doesn't really exist.

Of course, the answer is probably that the text is illegal in the US, because the DMCA overrides the first amendment. Whether the text includes the number or a link to the number, it all interferes with the ability of a company to make money, so it's illegal.


> If from a completely different domain, someone who has no relationship whatsoever to the maintainer of that first site creates a page explaining how DVD players contain AES keys and then links

The link is the illegal metadata. It's fine to explain that DVD players use cryptographic keys. It's fine to explain how said keys work. It's fine to have a list of prime numbers on your website for fun. It's not okay to link the two together. The link itself is exactly the type of illegal metadata I'm talking about.

Any type of pointing, eyebrow wiggling, coughing, etc. providing people with metadata on why certain numbers have cryptographic significance for a particular product is not okay (in my opinion).


That description can be embedded in the number. If you use ASCII it’ll be pretty obvious.

Encoding as a prime doesn’t impose any special requirements on the data. All you have to do is append a bit of junk to make the whole thing prime. The rest of it can be plain text or whatever.


> That description can be embedded in the number. If you use ASCII it’ll be pretty obvious.

In that case, the knowledge that information is encoded in that specific number and the drawing attention to that fact is the illegal metadata. In other words, numbers are just numbers - until you draw attention to specific numbers with metadata, that's when you cross the line.

If you make a website with a prominently displayed huge prime number with flashing lights and arrows, you've added illegal metadata that says "try decoding me" or "I am probably a cryptographic key to something"


That seems like a pretty loose definition of “metadata.” And the number would be illegal no matter which medium you distribute it with. The mere act of distributing it (or just possessing it) is enough.


Large numbers can mean anything depending on how you interpret them. If you provide the means (metadata) to interpret a given large number as illegal information (state secret, crypto key, etc.), why shouldn't that be illegal?


I'm not saying it shouldn't be illegal to provide the metadata needed to interpret a large number. I'm saying that lots of large numbers need no metadata to interpret them. For example, if you came across a number consisting of the raw text of this comment represented as ASCII and encoded with base 256, you'd easily be able to figure out what it said with no metadata at all. If this comment contained something illegal, then you'd easily be able to obtain that. Metadata isn't needed.


You'd still need to know that the number is a base 256 encoded string, and the chances you run across such a number in an innocent context (i.e. math publication) seems infinitesimal.

Someone who knowingly hosts a base-256 encoded secret should be held as accountable as if they had hosted the same information in picture form, morse code form, or plaintext.


Base 256 is plaintext. That’s just standard bytes.


The metadata in this case is the ability to read english text.


> How is it possible that a government can forbid information?

By having enough capacity for organised violence to make their will stick. And if they lose that, they are no longer a government.


A government can be defined as "a public organization for the systematic and systemic persecution and elimination of minorities"

The only major dispute between governments is which groups of minorities to target.


> A government can be defined as "a public organization for the systematic and systemic persecution and elimination of minorities"

Yes, but that would be a silly definition; governments rarely persecute as an end goal.

A more sensible one would be: a government is what controls a state, and a state is an organisation with a monopoly of legitimate force on an area of land.


Can you name a government that does not systemically and systematically persecute murderers? Pedophiles? Tax evaders? Drug users? The list goes on. Minorities are not limited to race, gender and the like.

The persecution perspective raises several ideas to the surface that get buried under the monopoly of force definition. The latter is concerned with collection of power, but the former is concerned with the use of power. Further, in countries such as the US, there are numerous arms among the citizens and the government cannot be truly said to have a monopoly of force (disproving the definition at least in part).

To what end is a monopoly of force? There is always a moral judgement in the use of power and always a line in the sand concerning who should be persecuted. Sometimes that line is murderers and sometimes it is homosexuality or saying things the majority disagree with.

Further, the persecution definition is more accurate in that it places the responsibility into the correct hands. Governments are formed by the people who consent to them and have no life of themselves. Even in a place like North Korea, most people endorse a government that most of us find horrible. The position of that line of persecution isn't determined solely by government fiat -- it is a result of the people's consent and inaction.

A government would find catching murderers impossible if the general population did not (as a majority) support and help them. Slaves would not have escaped from the South in any significant number if so many people in the North had not consented. Likewise, lynchings, kangaroo courts, and Jim Crow would not happen if the majority of people had not consented.

Very importantly, this view forces home the effects of intolerance. When a large group of people silence their opposition "freedom of speech isn't freedom from repercussions" they are in fact exercising this exact type of governmental persecution power, but without the tolerance that is otherwise "agreed" upon.

This raises what is (to me) the most interesting argument of all. Speaking of the US. We agree that the government cannot punish people for controversial, but non-inciteful speech. We are the government ("by the people"). We simultaneously agree that we can do the exact opposite in our personal lives and ruin someone we disagree with. This shows our true line in the sand is very much not in sync with the one we voted for and illustrates a very complex, but dangerous cognitive dissonance.

I could go on, but this lens is the most useful one I've seen for looking at how society, morality, and government interact.


Yes, this means jail time, fines, and executions of humans to enforce their will.

If they dont do this, no one cares about 'the law'.


> How is it possible that a government can forbid information?

I think that intent and plausibility play the most important roles here.

Also, if the number of bits you need to describe an illegal prime is of the same order as the number of bits in the prime itself, then you have a weak case.


Yep. A prime-based compression algorithm is possible, but if you don't store the whole number, it will take forever to calculate. How are you going to describe it? Are you going to say it's the Nth prime, so go ahead and calculate all (N-1) primes to find it? That's a lot of primes. And by that point it's not any different than sharing data with any other (sane) compression algorithms. Encoding information this way is really cool, but offers no advantages.


It won't work. There are 37,607,912,018 prime numbers smaller than 1,000,000,000,000. It's 11 decimal digits vs. 13. All the compression comes from the information that it is a prime number.

To point to the "Nth prime" would require almost as many digits as the prime itself. Mabe it's more efficient for very large primes, but I don't think so.


There are a lot of easily describable primes, like the Mersenne primes. A lot of numbers can be described in fewer bits than directly. This is not always the case, but you could just keep looking for another more easily describable prime or broaden the search space to include non-destructive modifications of the data you're representing.


This is just data compression. Most strings can’t be compressed, and nearly all strings can’t be compressed by more than a small amount.


>nearly all strings can’t be compressed by more than a small amount.

source?


https://en.m.wikipedia.org/wiki/Pigeonhole_principle

As you increase length, the number of possible strings grows exponentially. There are only a few (relatively) much smaller strings you can map to.


"It is a bit string" is true. "It is a top secret document" is also true. Why would the law look at only the first and not the second?

I sometimes make the joke that unicode sequences make people extremely angry. It's a gentle reminder not to take everything so seriously. But everyone still understands that it isn't actually the sequential placement of glyphs that make people angry.


Information can be used as a weapon. Government wants to control weapons and forbid it sometimes. I think that's an obvious answer.


I don't think it's a question of their reason but a question of feasibility.


Hey, we manage pretty well to get people to fill out complicated paper forms to calculate their taxes, so certainly it's feasible to enforce laws despite the obvious practical impossibility of actually physically forcing everyone to obey them.


Yeah, that's what happens when you threaten them to deprive them of their freedom, to torture, and to murder them. Perhaps you are so civilized you resort to fines first, but what if they decide to not pay said fine? Are you going to put them in prison? What if they resist being mugged and kidnapped? How are you going to get them to prison if they resist? I suggest you search for many instances of the IRS shooting innocent people, they literally have armed squads for that purpose, they flashbang babies, etc.

Are you really surprised that most of them comply? What other choice do they have?


Can information be used as a weapon?

Definition weapon - a thing designed or used for inflicting bodily harm or physical damage.


Are you sure that's the whole of the definition from the source you took it from? It looks suspiciously like a fragment of the definition on en.oxforddictionaries.com, omitting the part of the definition that is more general.

https://en.oxforddictionaries.com/definition/weapon


Yes. Consider a detailed blueprint for a physical weapon. Or information that make coordinated use of armed forces more efficient. Or blackmailing material.


As you've specified a weapon must be a thing, then trivially no, by definition.

But certainly information can be used for extortion, or to otherwise coerce people against their will, and maybe that's enough?


> As you've specified a weapon must be a thing, then trivially no

"Information" is a noun, hence it is a "thing".

Furthermore, the 'physical damage' it can inflict is the destruction or manipulation of physical memory cell states.


If you want to have the argument that a "thing" can mean "information" I wish you all the luck in getting a partner that agrees with you. Personally it's both for me, depending on the occasion.


There is no argument, "information" is a "thing", by definition.


I think information is likely more analogous to ammunition than to a weapon.

By itself, it is harmless, but when paired with an appropriate device, by a user with malicious intent, it can then be used to cause harm.


So psychological and material harm are irrelevant?


Are you really asking if it's possible to forbid information? It's possible because they have people with guns who will physically take you to jail. But maybe you mean: is it just? I'm generally libertarian-leaning, but there are obvious cases where the government has a legitimate interest in restricting some speech, and those categories are well-defined (although everyone debates on the margins, all the time).

Whenever this attempt at reductio-ad-absurdem comes up, I find it pretty unconvincing. It's not that they are banning a number, just like if you make certain images illegal you're not banning "light" and if you make slander illegal you're not banning "sound, which is just vibrations in the air." Describing the medium of speech is kind of silly, because the point is the information contained in the media. The fact that the law addresses abstract concepts isn't exactly groundbreaking.


"Information" is simply an abstraction of the physical world. The physical world that we experience and describe is simply a metaphor on top of that raw data.

Everything is information. How can murder be forbidden? It's just an arrangement of quarks?!


As pi is infinite, it also stores any imaginable information. Someone actually went ahead and implemented a file system based on this idea:

https://github.com/philipl/pifs


> As pi is infinite, it also stores any imaginable information.

Whether that is true is related to the normalness [1] of the number pi, but this property has not been proven. See also: [2].

[1] https://en.wikipedia.org/wiki/Normal_number

[2] http://www.askamathematician.com/2009/11/since-pi-is-infinit...


That was a fun read. Ive always thought about this when people say 'THE UNIVERSE IS INFINITE SO WE ARE EATING DINNER AT HELMS DEEP SOMEWHERE'.

Naw man, physics still apply, you dont get gandalf just because you went a few million light years toward Andromedia


There is a great Numberphile video loosely related to this (no magic though)

"Googol and Googolplex - Numberphile" - https://www.youtube.com/watch?v=8GEebx72-qs


The difference is that Pi is apparently normal, up to all extensive existing evidence. The Universe is not normal. Anyway, Physics doesn't preclude Helms Deep.


I think normalness is a stronger property than "possesses all sequences of the alphabet of its digits", since it means that + "all subsequences are equally likely"


He claims 100% compression, but that clearly disregards the digit ID which is potentially quite large to store. Any idea as to how to compute stats for actual compression (size(content)/size(index))?


Assuming that pi is a normal number [1], its digits are uniformly distributed. Therefore the density of a given binary sequence of length N in pi’s binary expansion is 2^-N.

So on average, the offset for a given binary sequence will be on the order of 2^N (I’ve used some hand-waving here). You need N bits for that, you you’ve gained basically nothing.

[1] https://en.m.wikipedia.org/wiki/Normal_number


A friend and I tried to do this in highschool and realized it wasn't so useful except for a cool factor.


I think reading a bit farther it becomes clear that it's a parody

Edited to fixed terrible spelling


You mean “parody.” This near-homophone is quite confusing here!


Oops. My only excuse, weak as it is. Is that I typed that on my phone. Fixing it now thanks.


Sure it is! It's an interesting problem nonetheless :-)


Size of the index would just be log2(index), right?


Your calculation works backward from already knowing the index.

I assume jgtrosh's question is more of a probability and estimation question. E.g. the string "Hello world" takes up 11 bytes and what's the size of the index into pi? To generalize a little more, to store any 11-byte sequence, what is the estimated size to store its index? To find the exact 256^11 byte sequence in pi, there will be many cases where the sizeof(index) is greater than the data itself.


Yes but index would be ~2^(length of content)


> He claims 100% compression, but that clearly disregards the digit ID which is potentially quite large to store

That reminds me of a compression program I once wrote. It had the following properties:

1. It accepts any non-empty file other than a file consisting of a single 0 byte.

2. It is easily reversible.

3. The output is never larger than the input.

4. The output is smaller than the input for some files.

5. If a file is larger than 1 byte, iterating enough times will always eventually produce a smaller file. What is "enough times" depends on the file content.

(I wrote this partly as a joke, and partly as a counterexample to some proofs I'd seen on Usenet about the limitations of compression programs where the proofs had not been sufficiently precise in specifying the conditions necessary for them to apply).

It is actually quite simple:

1. If the file is empty or a single byte that is 0, report that the input is not acceptable and exit.

2. If the file is N bytes, treat it as if it is an 8N bit unsigned integer, I.

3. If I is 0, the output file is N-1 bytes all with value 0xFF.

4. If I is not 0, subtract 1, and output the result.

(Decompression is left as an exercise for the reader).

Another way to look at this is to imagine that we have a sorted list of all possible files. The primary sort key is file size. The secondary sort key is the numerical value of the file when treated as an 8N bit unsigned integer, where N is the file size.

My compression algorithm is simply to replace each file with the file immediately ahead of it on that file list.

Viewed that way, it is pretty obvious that all my claims are true. It accepts any non-empty file other than the first file on the list (single 0 byte). To reverse it, replace the input with the file immediately after it from the list. The list is ordered by file size, so stepping down in the list never gives a larger file, and sometimes gives a smaller file. The output file is on the list, so you can obviously iterate.

The catch, of course, is that while yes, you can take your 1 TB of arbitrary data (even true random data!) and apply my algorithm iteratively to get down to, say, a 1 byte file, and yes, you can apply the decompression algorithm iteratively to recover your 1 TB from, to do that you have to know how many times to iterate on the decompression end.

The number of iterations required for an uncompressed file of N bytes to compress down to a byte is on the order of 2^(8N), so you will need about N bytes to store the iteration count.

So net result is that it can replace an N byte file with a 1 byte file...but it is going to drop N bytes of metadata on you that you'll need to store somewhere.


Undortunately with this solution you’re still storing the same amount of information as you’d normally do. It’s just encoded as offsets into pi’s decimal expansion. You can’t cheat entropy.


That's not necessarily true and probably is false. What we know about Pi is that it includes an infinite number of elements, but this says nothing about the structure of those elements. An infinitely long random sequence will probably hold every pattern possible (I'm not a mathematician so correct me if I'm wrong) but any structured or repeating sequence doesn't.


> An infinitely long random sequence will probably hold every pattern possible (I'm not a mathematician so correct me if I'm wrong) but any structured or repeating sequence doesn't.

This is not true. Pi is probably irrational, which means we know it doesn't repeat itself. However, it is not proven to be normal, so it's a conjecture (but not fact) that it contains every finite sequence of digits at some point.


That's the worst possible typo for this conversation.

Pi is provably irrational, and probably normal!


> That's the worst possible typo for this conversation.

Damn autocorrect! And it's too late to edit it, too.

Yes, that should say "provably irrational".


Can pi be recursive then? Can it contain itself? I think not.


No. If pi would contain itself it would be a rational number. We have a proof that pi is irrational, hence it cannot contain itself.


Specifically, if pi contains itself, that means "pi - pi/b^k" is a terminating fraction N in base b", where b is your choice of base (like base 10), and k is some positive integer. So

pi = N/(1-b^k) which is rational.

(And if you set k=0, you get that pi "contains itself" in the sense that pi from the 1st digit onward is of course pi)


> Can it contain itself?

Well it does, trivially.

You’re probably thinking of set theory but the file system is about storing information in a sequence and an offset. Seen that way, π can be stored with offset 0.


If it's normal then it contains all finite strings uniformly in its base-b expansions. Pi is not a finite string so it wouldn't have to contain itself uniformly. More specifically if it contains itself then it's a rational number, but we know that pi is not a rational number. Note that we don't know whether pi is a normal real number.


To be fair, no other filesystem could contain pi either, right?


How do you even calculate pi with such accuracy?



This is brilliant, thank you!

edit: am I the only one who thinks that this whole pifs filesystem was meant as a joke?


Everyone knows it is a joke.


Beware of technology-generated outrage. If you can encode a message, image, etc. as a number, some messages, like a communication of a specific threat against a specific person, or certain types of porn, that's going to result in "illegal numbers." When put that way, the outrage is pretty weak.

It is legitimate and provably effective to legally limit the demand for some items, like ivory, for example, by making it contraband, interdicting trade, and punishing possession.

So what is the outrage actually about? A lot of it is about corporations asserting property rights in publishing and enforcing those supposed rights in ways that result in bad decisions, bad designs, bad products, insecure systems, and bad uses of law enforcement related to computing.

The solution isn't to "make all numbers legal" because that's not the question. The solution is to address the problems in the real world, where they make sense. Limit copyright terms. Limit laws to publisher-scale theft for profit. And that boils down to nerfing corporate money in politics.


>It is legitimate and provably effective to legally limit the demand for some items, like ivory, for example

Whats the proof then? Last I checked, despite all laws, ivory animals are being poached into extinction. It might be more effective than doing something like paying poachers to poach even more animals, but that isn't proof it is an effective means to stopping the problem of poaching animals into extinction.


Ultimately this is totally nonsensical because you'd have to ban an infinite number of number because some clever boy around will definitively distribute the number preceding the illegal one and some unrelated folk can point out that you just have to +1 to get the illegal one. Basically none of the two would have done anything illegal until a ruling. rince, repeat. This is utter non-sense.


> This is utter non-sense

All current computer media can be represented as an integer. You're suggesting that no media is illegal?


It shouldn't be illegal. Possession of information - be it a book, a video, a picture, or text, should never be illegal in itself. Production and distribution of certain kinds should be absolutely illegal, but they already are, I don't think there's any discussion here.


> Possession of information [...] should never be illegal in itself.

It certainly makes for an interesting discussion, however, your view is fringe here -- the laws of virtually every free democracy on the planet encapsulate the idea of some information being illegal.

HOWEVER: the gp point wasn't coming at it from your perspective there. They were saying (as I understood it) the fact that integers are "just numbers" meant that banning them was nonsensical. By extension, the illegality of distributing them would also be nonsensical.


> the laws of virtually every free democracy on the planet encapsulate the idea of some information being illegal.

Illegal to disseminate, not to own. There should be no punishment for being able to access or possessing information; Liability should squarely sit with the publisher, intentional or otherwise.


Most places have indecency laws which cover things like video of murders and extreme pornography; privacy laws that make acquisition and retention of data/imagery illegal; etc..


We (you) are conflating issues. Creating, distributing, profiting from, and possessing are all separate issues. Possession of information of any kind should not be illegal, as information is in and of itself not harmful; It's how you use it which should confer liability. If I download instructions on making a nuke, for example, that shouldn't be illegal. It should be illegal to make a nuke, to use a nuke, and to distribute them onward, but not to own them.


>If I download instructions on making a nuke, for example, that shouldn't be illegal. It should be illegal to make a nuke, to use a nuke, and to distribute them onward, but not to own them. //

According to your assessment here you're an accessory to a crime - a willing and necessary participant. You said (hypothetically) you downloaded it, but that distribution should be illegal. Distribution and reception are linked, you can't get it without the distribution.

Demand for distribution fuels the supply.

I absolutely would maintain the illegality of ownership of some types of information (mitigations aside) - child pornography, imagery of rape or assault are obvious ones.

Freely allowing the supply and acquisition of details on making nukes is fine, because acquiring the components is difficult and can be controlled.

My quandary is that I want to be liberal to allow curiosity and educational intent to be fulfilled; but realise that there are elements who abuse the free acquisition of information that enables great harm (how to make a fertiliser bomb, how to make ricin).


Most judicial systems would conclude that if for example you had extreme snuff porn on your computer, or the private personal records of another person, that there could be no legitimate procedure by which you could have obtained them. I don't think claiming that you extracted them from Pi, or 'could have done so' would be taken seriously as a defence.

The law for all it's flaws is ultimately a practical discipline, not abstract logic. Unless you're against all laws in general, which is a thing for some people.


Interestingly enough, in the US, for the specific case of nuclear weapons design information, you don't even have to download it for it to be illegal. This class of information ("Restricted Data" as defined by the Atomic Energy Act) is "born secret" - even if you write it yourself, you're not allowed to have it.

(It should be pointed out that it's not been shown that this would actually be upheld by the courts).


If anybody is conflating things, it's you. And what you seem to be conflating is the meaning of the word "is", with that of the word "should".

You might be quite right in that no information should be illegal to posses. That, however, does not make it so. There's plenty of information that is illegal to posses. The fact that you don't like it doesn't make it less so.


If possession is not illegal, why is distribution? You point makes no sense.

Consider your argument with respect to privacy and data issues - obviously possession of information can be in and of itself harmful because it can be something that other people have a right to restrict your access to.


Would you be okay with someone possessing nude photos of yourself? After all, "holding information isn't in itself harmful", as you state. What about, god forbid, pornography starring your underage child. Is it still "just information"?


If I make those photos available then yes, of course I would be happy. If they were taken without my consent, that is different. If I do not take adequate measures to protect them from accidental or malicious release, that is also different. I am specifically saying that owning knowledge should not be illegal. Creation, distribution, profiting from... All different things. Possession of data at rest should not be a crime, regardless of content. It's what's done with it that changes legality, in my opinion.


That's reducing things to a logical extreme and removing all considerations of practicality. In the end, that's not a good way to look at law, or the nitty-gritty of the world for that matter. If you find someone with nude photos of yourself, and you didn't give them to them, then you can conclude that those photos were obtained illegally. That fixation on the distinction between "technically just posession" and "creation/distribution/etc." is not really helpful.


Being a reasonable person, I don't see any reason I would care if someone has nude photos of myself, even if I was a child at the time the photos was taken. The photos are not harming me, nor will they be harmful to me in any sense other than random chance. I know there is a photo of me pissing into the sea when I was young, it doesn't bother me a bit.


It's good that you don't care, but don't I (or anyone else) have a right to care and not want those photos?

And I don't believe that you wholly don't care. I'm almost certain you must have some photos, or potentially may have some situations, if you were photographed, that are embarrassing and that you wouldn't want the general public (parents, coworkers, boss) to see.


Did he say that you don't have the right to care? He did not.

You can care, you may not want these photos to be where they are, and you may attempt to have them removed if it is possible, but you don't have the right to punish people for not caring, and you don't have the right to force people to care for the things you do.

I personally hate being on photos, so I try to avoid it to my best ability. I also asked someone to have a photo of me removed from somewhere. This is all understandable. The problem occurs when you are trying to dictate other people's lives by threatening to use violence against them for not conforming to your beliefs, etc. No need to resort to violence, come on.

I have a feeling you would attempt to beat me up for my tone alone because you perceive it to be hostile. Not cool. :P


Under current law that is already legal as long as they hold copyright. There is a grey area deciding what is artistic and what is prurient, but if ruled artistic, they could publish it in a book and sale in on Amazon.

But I think we should consider a major division between the rules of sharing information and the rules of possessing information. If I know how to make something bad, that shouldn't be wrong. If I share that for the sake of a discussion, that shouldn't be wrong. If I share it with someone who will use it to cause harm, knowingly aiding them in causing harm... well isn't that where we should say wrong has been done?


[flagged]


You shouldn't care about people possessing child pornography, because if you do then it's because you should have "paid more attention to your kid and improved your parenting". Got it. Have a nice day then.

EDIT: I know I shouldn't reply to trolls, but your drivel ticked me off so, dumb as I am, I'm going to respond.

Yes, criminalizing possession of child pornography reduces the consumption, and therefore demand, of said child pornography. I'm sorry if this offends you, or that you think your "freedom" (to own child porn?) is threatened by this, but I rather think reducing the number of child abuse cases is a worthier goal than stroking your misplaced sense of worth.

>What next, are you going to make the government threaten to kill others if they refuse to feed your kid through taxation because you bred despite the fact you are unable to feed your kid?

Oh you're one of those guys. You just couldn't resist the urge to shoehorn your agenda and announce at the top of your lungs: "look at me guys! I'm rugged and tough and I don't care about your kids! I am so smart!".

>many perverts on the Internet are probably also masturbating to these photos

That I don't give a shit about, and I never said that I did, so you can store your straw man back in the cupboard. What I care about is measurable decreases in demand for child abuse content that are the result of criminalization of possession.

Finally, kindly knock off your stupid fucking derisive tone. I would wager a considerable amount of money that you wouldn't talk like that in person, with anybody.


> You shouldn't care about people possessing child pornography, because if you do then it's because you should have "paid more attention to your kid and improved your parenting".

You are right; I don't care. You might possess illegal tactical plants: I don't care. Why should I?

> Yes, criminalizing possession of child pornography reduces the consumption, and therefore demand, of said child pornography.

Citation needed. I believe it's false on the same principles that apply to illegal substances. Criminalizing possession of illegal substances do NOT reduce the consumption, and do NOT reduce demand. I'm willing to change my view on this in presence of reliable evidence to support your claims. I somehow doubt if you were to revoke those laws you would see an increase in demand.

> I rather think reducing the number of child abuse cases is a worthier goal than stroking your misplaced sense of worth.

You are making the false assumption that possession of child pornography necessarily lead to child abuse, i.e. actual physical violence which I am deeply against. I need citation to support the claim that child pornography laws regarding possession of such do indeed significantly reduce the number of child abuses, and that possession of child pornography usually lead to child abuse.

Additionally, what constitutes child pornography varies greatly between places: https://en.wikipedia.org/wiki/Laws_regarding_child_pornograp....

On another note: I hope you are aware of child neglect being a form of child abuse, which involves the lack of attention and safety of your offspring. You are responsible for your kid and nothing you say will change that. Please do educate yourself on child development and parenting as required. I know I would.

> I'm sorry if this offends you, or that you think your "freedom" (to own child porn?) is threatened by this

I know you are not sorry, but in any case: don't worry; I'm not offended, however, please save me from your covert and false accusations.

> Oh you're one of those guys. You just couldn't resist the urge to shoehorn your agenda and announce at the top of your lungs: "look at me guys! I'm rugged and tough and I don't care about your kids! I am so smart!".

Please save me from your evidently false accusations. If anything, I seem to be caring more about your offspring than you do. Read my previous comments. I'm literally straight out bashing lousy parents and telling them to pay more attention to their children and so on. People down-voted it. How is this in any way an indication of me not caring about your kids? You seem to be really confused.

> A: "Please pay more attention to your kid, improve your parenting as needed. Make sure your kid is safe, educate your kid of the risks and potential consequences of sharing photos on the Internet, etc. If you are not financially stable and you are unlikely to be able to feed your potential future kid, please use contraceptives instead or something."

> B: "You troll, you don't care about our kids! down-votes A's previous post"

You are hilarious. This is some serious cognitive dissonance, can't make this up.

> What I care about is measurable decreases in demand for child abuse content that are the result of criminalization [sic] of possession.

Citation needed.

> Finally, kindly knock off your stupid fucking derisive tone. I would wager a considerable amount of money that you wouldn't talk like that in person, with anybody.

You mean perceived (by you, and possibly others) derisive tone? Adding the word "kindly" does not make your sentence any less threatening where the threat may be non-existent but is still perceived by me. Please do re-read your comment and focus on evaluating YOUR tone while you are at it, as you don't seem to be doing any better. It's not an excuse, but unlike you, I'm not offended nor care about your tone which in no way invalidates anything you say. I care about content.

> EDIT: I know I shouldn't reply to trolls, but your drivel ticked me off so, dumb as I am, I'm going to respond.

I put a warning for you, did you deliberately ignore it? Make no mistake, I don't mind that you are going to lose sleep over it, I just find it perplexing. Imagine you have epilepsy: are you going to ignore the warning that says "The following video contains flashing lights that may trigger seizures in individuals with epilepsy"? Are you going to call the person uploading the video a troll, too?


> Possession of information of any kind should not be illegal, as information is in and of itself not harmful;

And how does one come to possess information without creating or receiving (distributing) it?


This is about distribution. The whole concept of media is inherently related to distribution (of information). It's in the very etymology of the word.


Absolutely, but to use books as the example here - should we ever send people to jail for owning a book? Like, just sitting in their home library - should you ever go to jail for one? If yes, why yes? If no, what if the book is Mein Kampf? What if it contains graphic descriptions of child rape? What if it contains nuclear codes for US army stockpile? What if it describes how to make bombs and conduct terrorist attacks?

Or maybe....we should look at who is distributing material that we have a problem with, and target it there? As a society we should never be putting people in jail for just owning a certain piece of information, would you not agree?


> If no, what if the book is Mein Kampf?

Incidentally there isn’t a single country (as far as I could find) where owning Mein Kampf is or was illegal. There’s a common misconception that its possession is or was illegal in Germany. However, this was never the case. Until 2016 the state of Bavaria owned the exclusive copyright and prohibited its publication. But that’s it.


That's kind of my point - Owning it is not a crime. If police finds a copy in your house, you're not automatically going to jail just because you have it. At the same time, its publication and sale is either prohibited because of copyright issues or under laws which prevent sale of Nazi paraphernalia.


Fair enough. I was just adding this trivia since the item stuck out of your list: all the other items may (under some jurisdictions) be illegal to possess.


If someone has videos of child rape on their hard drive, do you think they should be arrested and charged with a crime?


Nope, unless they participated in creation of such video. If they just downloaded it off the internet, then no - maybe they should be sent for mandatory psychiatric evaluation, but to prison? No.

Let me put it this way - you can go on google right now, type in "two teenagers kill man with screwdriver", and very quickly(on dailymotion) find an EXTREMELY graphic video of two guys killing a person with a screwdriver, picking out his eyeball and playing with it, while he's still alive etc etc. It's absolutely sickening and it shows a horrendous crime being committed. Yet watching and/or downloading such a video is not a crime in itself. If police ever found such a video on your drive they would probably go "wtf dude" but nothing would happen to you. How is that different from the video you described? Because someone might wank to it? What if someone gets off on the one I described? Is it a crime before or after you get aroused?

Instead, like I said - simply having a video/picture/text/drawing of literally anything shouldn't be a crime in itself.


The reason for criminalizing ownership of child pornography is not just fighting about vice. It's also understanding that people consuming such media are creating demand for it, and where there is demand, there soon is also supply. Because child sexual abuse is considered to be a horrible thing, fight against people who commit that abuse happens both at the supply and demand end.


I'm not sure this is actually true - but if you have sources, I would happily give them a read. It seems almost common sense that pedophiles abuse children because they want to abuse children. It gives them pleasure, so they do it - if they create a video at the same time, it's almost incidental. Unless we assume that there are people out there who wouldn't normally abuse a child, but they do it because they want to make a video and put it on the internet - then yes, demand for such videos creates supply. I find that unlikely though.


That actually is often why they do it. Obviously, they are also sexually attracted to children and are evil. Those two are also requirements, but the third is the audience.

Consider this - how many people do you think make YouTube style vlogs then DON'T upload them to YouTube? Not many right - the audience is part of the inventive for making the video. Among paedophile communities first generation IIOC are highly prized.

Source: I am a criminal investigator who works exclusively on CSE


But if they are sexually attracted to children and are "evil", then the creation of the videos and photos are just a "side-effect", the abuse probably would have taken place regardless, right? I had people telling me that possession of child pornography leads to child abuse, what do you think? I watch gore videos[1] sometimes online and I don't want to hurt people. I watch them to remind me that there are many violent people and places out there, that not everything is butterflies and sunshine. It makes me introspect. It makes me value the society that I live in that shelters me, and makes me realize how lucky I am.

EDIT: Actually, I'm trying to come up with reasons that apply to child pornography but without any success. Not saying that they are not going to offer you a "reasonable" insight, but at this moment I can't think of anything. Perhaps something anatomy related? Medical value/curiosity?

On another note: yeah, people do crazy shit for the likes and subscribers, it's pathetic and sickening. All those challenges, etc. Ugh. I try to avoid that side of the Internet. Is it just me or is there really a decline? Yesterday I read how in UK schools they had to remove analog clocks because kids couldn't tell the time off it.

I don't know, I know so many parents who are doing a great job. Their kids don't care much about social media, they are not interested in getting likes, not interested in being YouTubers, know the potential dangers of the Internet, and so on.

[1] Albeit I don't download them, but at the same time you can probably do the same with child pornography, though from a technical point of view you probably have them cached which could be considered possession I guess.


Isn't the possession of eg. pedophile drawings, or (theoretically) CGI / AI-generated pedophile movies also criminalized?


Ah, finally someone with a more positive tone (in contrast to mine) and a better way to articulate my thoughts. Thanks. :)


I don't see the problem with banning or otherwise regulating certain representations if that is a useful tool against the production you are trying to stop.

This sort of "everything is allowed" arguments just seems like a way to avoid having to think carefully about what restrictions are reasonable, and what constitutes responsible use of information. Simply lazy irresponsibility.


Except it's not "everything is allowed", and the "ban and regulate everything" mentality seems to be more harmful, useless, waste of time and money in reality.

Regarding responsibility: https://news.ycombinator.com/item?id=16933814


I have commented before about A/B testing the law to achieve statistical outcomes, and I absolutely do see a problem with it. It tosses principles and liberties out the window. Legislating things that are correlated with the thing you want to avoid is a utilitarian bridge too far for me.


So you'll be fine with DUI? After all, it's not the alcohol we're trying to avoid - it's the accidents, which are correlated with alcohol (for obvious reasons).

Truth is, often correlations are the only things we can go after to fight the things we don't want.


I think that reaching for legislation as the tool to minmax any desirable societal metric is a bad doctrine. That does not mean I am against every possible instance of it. DUI is very immediate. It's like putting one round in the chamber and pointing it at a public space. But, for example, I am opposed to restricting speech and free association as a less expensive proxy for stopping various things.


Should possession of anything be illegal?


Sadly, being silly doesn’t make a law unenforceable (for example, every Witchcraft Act).

There is a lot of content out there which is illegal to possess, not just DMCA circumvention, and thanks to the wonderful power of mathematics that content can always be expressed as a number.

Extending your analogy, you could have a random bit sequence, XOR it with the content and distribute only the random sequence and the XORed sequence, making it a nonce-sense.


Or you could use a public and well-defined bit sequence, such as binary digits of pi, and distribute the XORed sequence.

You might even decline to mention which well-defined bit sequence you used, and just leave it as an exercise for the reader to try XORing with pi, e, phi, sqrt(2), etcetera on their own.


Being a contributor or accessory to crime is also ordinarily punishable and accounts for this.


The map is not the territory. The mathematical model for reality is not reality.


Hahahahaha. Related: https://en.wikipedia.org/wiki/Illegal_number

> An illegal number is a number that represents information which is illegal to possess, utter, propagate, or otherwise transmit in some legal jurisdiction. Any piece of digital information is representable as a number; consequently, if communicating a specific set of information is illegal in some way, then the number may be illegal as well.


This was an illuminating read. I was not at all aware that there are certain numbers(!) that are illegal. Thanks for sharing


Well, I'm not sure it's fair to say the number itself is illegal: it's the code that breaks the law, the number just happens to be one way to express it.

A perfectly equivalent statement is that there are certain "strings that are illegal", but this is both trivially true and a clearly exposes the fallacy at play here.

A written death threat is still a death treat no matter the string encoding you use, so while yes it is an "illegal string", this is just incidental: its the threat that the string encodes that is really breaking the law.


Not really disagreeing with you, but taking it even further:

A "written death threat" is not "illegal". I've seen plenty of such threats written on the boundaries of military sites or even electricity substations. Delivering death threats to a person may constitute illegal harassment, but so might delivering love letters. It all depends on the circumstances.


A warning is not the same thing as the sort of threat you get in trouble for. If the circumstances are 'conflating the meaning of terms' then yes, a lot of things - practically everything - can end up 'illegal'.


In much the same way that the word “fire” itself is not illegal, but shouting it in a crowded theatre may be.


No. Ken "Popehat" White wants you to read this:

https://www.popehat.com/2012/09/19/three-generations-of-a-ha...

Please use different phrasing to discuss lawful and unlawful speech in the future.


Everything is a number. When you think of an illegal media, such as child porn, it is in fact a gigantic number that your computer parses and turns into an array of frames which is an array of Red, Green, Blue values. Since everything can be encoded into numbers, and some things are illegal, trivially some numbers are illegal (in certain contexts).


This was clearly not written by a lawyer. I am also not a lawyer but it's pretty clear that merely distributing this prime number is not illegal. Distributing it with the intent to use it to use it as DeCSS may be though. And it would be pretty hard to convince a judge that you didn't intent to use it as DeCSS.


I don't know about DeCSS in particular, but plenty of laws are strict liability meaning intent is not required to obtain a conviction.

> And it would be pretty hard to convince a judge that you didn't intent to use it as DeCSS.

so "merely distributing this prime number is not illegal" is de facto illegal.


Supposedly the prosecution - in an English-style law system - has to convince the court beyond reasonable doubt that it was intended to be used for wrong.


It’s illegal because it’s someones job to enforce it, they probably don’t get paid much, and they have many bills to pay. And every now and then they can impress chicks by saying they manage national security. And the department who monitors us for usage of this number using all the latest expensive tech and expertise, can charge it to the tax payer. Just imagine if the number got into the hands of the enemy. ka, ching, that will be another billion dollars for my top secret department thanks very much.


Surely there must be a shorter number or string that I can put in my personal information that would be illegal to copy or store. I am ok with being in trouble for having the data, as long as everyone else with the data is in trouble as well.


So if I surreptitiously install a camera in your house and take pictures or video, then tweak the files so that their binary images denote prime numbers, all is cool; I'm just doing math, not invading your privacy.


So, is this the right thread to mention the honorable First Prime of Apophis? He did a few illegal things...


Is it of any particular relevance that such a number is a prime?


Large prime numbers are crucial for public key cryptography to function.


A large prime is notable and hence is included in public databases.


That's not really true. There are loads of large primes (way more than you could store), so they're not all notable.


Perhaps I shouldn't have said "large" or "notable". The point is that when a prime number is discovered meeting certain criteria it is included in public databases. This makes the case of an "illegal" such prime interesting.


There are infinite prime numbers. What's notable is the ones we have found.


No. Even then they're not notable. For example there are 10^97.6 primes with 100 digits, of which not all have been found (not enough storage space in the universe), but it's trivially easy to generate one at random.


You disagreed with the statement

> A large prime is notable and hence is included in public databases.

It is verifiably true that these public databases exist (bigprimes.net)

I'm not sure what you're arguing here.


I'm arguing that these numbers aren't notable just because they are large primes. They certainly aren't included in public databases just because they are large primes.

The example site you gave bigprimes.net has one main database, that includes the first 1.4 billion primes. These are all much smaller than the illegal primes mentioned on the wikipedia page (they have at most 11 digits, whereas the ones mentioned on wikipedia have 1000s of digits). It also has a list of the Mersenne primes, which are the largest known primes. The largest has 23249425 digits.

So primes with 11 digits or fewer are notable (because they are small), and primes with 23249425 digits or more are notable (because they are large), but primes with around 2000 digits are not notable.


Ok, thanks for explaining that. It sounds like the condition for notability in this case is the combination of size and algorithm used?

> Carmody created a 1905-digit prime, of the form k·256211 + 99, that was the tenth largest prime found using ECPP, a remarkable achievement by itself and worthy of being published on the lists of the highest prime numbers.


Oh, I didn't realize the page said that. I should have read it more carefully. You're right that it's a combination of size and method used. The Mersenne numbers are especially easy to prove prime, so it's also interesting to keep track of the largest primes proved by other methods. I think these days a 2000 digit prime wouldn't be notable in any case, but it sounds like it was back when Carmody was doing this, so this was in fact a good example of an illegal number that was independently interesting.


Another pointless argument that could have been avoided by RTFA.


Found the Wikipedia Deletionist.


I'm generally an inclusionist, but Wikipedia doesn't have enough server space to store pages on every known prime.


This could be used to circumvent other (all?) limitations of speech. Just say "look up the nth prime and unzip it" instead of what you can't say...

There should be a whole industry about it.


Calculating the nth prime is hard, but you may be interested in πfs, a system for storing and retrieving your data based only on the digits of pi.

https://github.com/philipl/pifs


This already exists, it’s called cryptography: for example, you can exchange some prime numbers (key exchange), and then use those to apply a generic mathematical function to the information. You then send the resulting numbers. (In this situation it isn’t the prime numbers themselves which are illegal, it’s the other numbers.)

Doesn’t change the legal situation, of course.


No, this is really not similar to cryptography. More like the opposite.

Cryptography is about exchanging secrets on an insecure network.

This is about legally publishing information you're not allowed to make public.

It does change the legal situation because, from the article, it's about

> ... the representation of the illegal code in a form that had an intrinsically archivable quality. (...) The primality of a number is a fundamental property of number theory and is therefore not dependent on legal definitions of any particular jurisdiction.


It's not less unlawful just because you express it in a number - just harder to catch. Surely there are easier ways to circumvent?


Expressing n is as hard as expressing the original data.


I remember the news about the example used in the post. This is a proof of a society where 50% loves math and the rest makes money with who loves math.


I always felt that that "illegal numbers" is a misunderstanding of data.

There are no illegal numbers. But if you provide context, they can become illegal data. Let's take child pornography for an example, because that's universally accepted as illegal. I could come up with a formula which translates a huge number into a bitmap. I could post the number (i.e. the input for the formula) online, because it is absolutely meaningless to anyone else. But when I publish my formula, it is no longer a number. It's data which can be interpreted as something meaningful, an image.

Everything is just a number without context.


https://en.wikipedia.org/wiki/Illegal_number :>

You can literally arbitrarily associate any number to anything and ban it based on that, which they did:

> In 2012, it was reported that the numbers 89, 6, and 4 each became banned search terms on search engines in China, because of the date (1989-06-04) of the June Fourth Massacre in Tiananmen Square.

> Due to the association with gangs, in 2012 a school district in Colorado banned the wearing of jerseys that bore the numbers 18, 14, or 13 (or the reverse, 81, 41, or 31).

> In 2017, far-right Slovak politician Marian Kotleba was criminally charged for donating 1,488 euro to a charity.

It's closely related to hate speech laws where the only requirement is perceived threat. Fun times. :D


That's why the Tiananmen Square Maassacre anniversary date is commonly referred to as "May 35th".

Banning specific representations of an idea is a game of whack-a-mole. As soon as you ban one symbolic representation, a new one will be created.


The Chinese government isn't stupid. They do what they do because it works. Even the opposition agrees with this, hence the term

https://en.wikipedia.org/wiki/Chilling_effect

The website dedicated to the topic of the OP article is even called... http://chillingeffects.org/ (since renamed to https://lumendatabase.org/ )




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